In view of the limitations of the traditional Brillouin optical time domain analysis (BOTDA) system such as low sampling rate, large transmission and storage space, a fast BOTDA scheme based on compressed sensing technology has been proposed to realize the random frequency sampling of Brillouin gain spectrum (BGS). The proposed scheme uses a data-adaptive sparse base obtained by the principle component analysis algorithm to realize the sparse representation of Brillouin spectrum. Then, it can be reconstructed successfully with orthogonal matching-pursuit algorithm. Compared with the traditional uniform spectrum sampling with a step size of 4 MHz, the proposed compressed sampling scheme can recover the BGS using 30% of the frequency. With fewer sampling frequencies, compressed sensing technology can improve the sensing performance of traditional fast BOTDA, including increasing the sampling rate by 3.3 times and reducing the amount of data storage by 70%.
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